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Continuous Euclidean Embeddings of Incomplete Preferences

See on Scoop.itBounded Rationality and Beyond

Abstract: Debreu’s classic theorem asserts that when an agent’s weak preference ordering is reflexive, transitive, and closed in a suitable topology, it can be represented by a continuous utility function. Of interest in some economic settings is to weaken these conditions by replacing transitivity with negative transitivity. Such preferences have been successfully modeled using multi-utility representations, ie. an order embedding into $mathbb{R}^n$ rather than simply $mathbb{R}$. Here we show that the topological conditions for a continuous single utility representation are sufficient to guarantee a continuous multi-utility representation, closing a conjecture of Nishimura & Ok (2015). The impossibility of a multi-utility representation consistent with Pareto improvement is also demonstrated.

See on arxiv.org



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agosto: 2015
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